1. Field
The described technology relates to systems and methods of generating continuous surfaces from data of a polygonal model provided, from, for example, a 3-D polygonal or Subdivision surface (Sub-D) modeling tool.
2. Description of the Related Technology
Polygonal model data is created with, for example, a 3-D CAD software tool by, for example, a designer. The polygonal model or polygonal mesh includes discrete data points describing one or more surfaces or objects. Polygonal models are convenient for design work at least because they define the surface or object at a degree of detail convenient for the designer to work with. The shape of the surface or object is defined by the data points, and the surface between the data points is perceived, but is not represented in the data. This allows for the CAD system to function quicker because of a significantly reduced data set representing the surface or object, while providing the designer enough detail to manipulate to achieve a desired design.
Once the designer has finished the design, the polygonal data can be used, for example, as the basis for manufacturing a physical object or for generating an image of the designed object. To manufacture the object, or analyze it, or to generate the image, the mesh data is often not sufficient. For a physical object or a realistic image, a BREP object containing one or more surfaces must be defined. The surfaces are preferably Non-uniform rational B-spline (NURBS). NURBS is a mathematical model commonly used to represent curves and surfaces, which are either analytic or freeform. A BREP (Boundary REPresentation) may be understood to be a geometric and topological representation used, for example, in CAD applications that links together curves and surfaces to form either a solid (closed volume) or a shell (open).
For accurate CAD models, the continuity of the interior surface and the continuity between adjacent surfaces are important characteristics of the final product. Mathematically, for adjoining surfaces, continuity grades of G1 and G2 are defined. Each point on the final BREP object is a point on one or more surfaces. The continuity of the two surfaces at a point where they touch is characterized as G1 if the surfaces share a common tangent plane at the point. The continuity of two surfaces at the point is characterized as G2 if the surfaces share both a common tangent plane and common curvature at the point. For high quality surfaces G2 continuity at most points on the BREP object is highly desirable in terms of design aesthetics and manufacturability.